first, 머물었다(x)->머물렀다(O) 머물렀다 is past tense so, I use the word'머무르다' instead '머물렀다' in this time. well.. 머물렀다 and 묵다 is often used in almost same meaning... but, 머무르다(the root of 머물렀다) means "stay or live temporarily(short period)", also it means "stop at the point" sometimes.(just a few minutes or hours is also okay) 묵다 is usually used in the situation as you stay the hotel or friends house or something.(sleep at some place or...)